WASHINGTON — What happens when the leader of the free world meets the leader of the hip-hop world?

All eyes turn to a beautiful woman, of course.

In fact, maybe Benjamin Netanyahu would have more luck if he could rock a red dress like this.

President Obama made time to chat with a stunning Beyoncé and dapper Jay-Z at a campaign fund-raiser Tuesday night — even though he’s not making time for a sit-down in New York next week with the Israeli PM to discuss the Iran nuclear threat.

Obama yesterday sent out the photo, which was taken at Jay-Z’s 40/40 nightclub in the Flatiron District.

“Cool pic Obama just tweeted of him with Jay and Beyoncé,” tweeted hip-hop mogul Russell Simmons.

The fund-raiser hauled in about $4 million for Obama and the Democrats. Guests, who included Yankee ace pitcher CC Sabathia, sipped $800-per-bottle Armand de Brignac champagne.

“Beyoncé could not be a better role model for my girls,” Obama told the crowd.

The president said he and Jay-Z have a lot in common: “We both have daughters and our wives are more popular than we are.”

But relations are still frosty with Netanyahu, who, according to an Israeli source, sought a meeting with Obama in New York, where the UN General Assembly meets next week, or in Washington.

The White House blames scheduling: the two leaders won’t be in New York at the same time.

But facing criticism for not meeting the Israeli leader, Obama called Netanyahu for an hourlong conversation that did little to soothe raw nerves.